# Re: Is a function a relation?

Date: Tue, 23 Jun 2009 04:17:14 -0700 (PDT)

Message-ID: <5067020c-97c0-4a8b-9764-a4ed3e852d83_at_3g2000yqk.googlegroups.com>

On 23 juin, 12:33, David BL <davi..._at_iinet.net.au> wrote:

> On Jun 23, 4:34 pm, Cimode <cim..._at_hotmail.com> wrote:

*>
**>
**>
**>
**>
**> > On 23 juin, 08:14, David BL <davi..._at_iinet.net.au> wrote:> On Jun 23, 1:35 pm, David BL <davi..._at_iinet.net.au> wrote:
**>
**> > > > Yes that's one way of looking at it.
**>
**> > > I'll expand on what I mean by that. It seems to me that one could use
**> > > special conventions to "show" that just about any type can be regarded
**> > > as a specialisation of a relation. E.g. one could say that a whole
**> > > number in [0,255] is a relation by introducing symbols to represent
**> > > 1,2,4,8,...,128 and the relation records a set of symbols that are
**> > > then interpreted in the manner of an 8 bit unsigned representation.
**>
**> > Relations is a possible construct that can represent *any* type if we
**> > are to consider that a type is a set of values. Nevertherless, a
**> > logical computing model (to define among other things the physical
**> > reprentation of domain values) must be defined first (that is what I
**> > spent the last 10 years working onto)...Hope this helps...
**>
**> It could be thought that the logical can only exist as an abstraction
**> over the physical. However I don't believe that's a useful way to
**> think. In fact I suggest it misses the idea behind physical
**> independence. What I mean is that the logical doesn't need to be
**> "realised" or "reified" by the physical at all!
**>
**> This could be seen as just a metaphysical comment (more specifically
**> in favour of mathematical realism), but what I really mean is that
**> pure mathematical systems can for example define things like the
**> integers in a way that's unique up to isomorphism through the
**> axiomatic approach, and that perspective is all one needs at the
**> logical level. I don't see how the physical comes into it at all.
**> Putting it another way (using the language of a mathematical realist
**> in denial), database values don't exist in time and space!
*

> It's not clear that type systems particularly help in this purist

*> mathematical endeavour.
*

The problem of achieving physical/logical independence under the
assumption of RMis far more complex than a simple taxonomy exercice.
The need for a specialized computing model is a prerequisite for
implementing relational logical operations.

The computing model must both take into considerations physical limitations of current systems while allowing sound representation of logical relational operations.

> I note that the usual axioms of set theory

*> completely ignore any concept of type. I'd be interested to know
**> whether modern mathematicians that have researched type theory believe
**> it's important to mathematical foundations. My understanding is that
**> Russell only investigated type theory with the aim to avoid paradoxes
**> by preventing loops, but his work was made redundant by axiomatic
**> systems like ZFC which is believed to be free of paradoxes.
*

RM is a part of set theory. Domains are in fact types that are
defined in a naive way.
Received on Tue Jun 23 2009 - 13:17:14 CEST